a model giving the conformation of a star shaped polymer is proposed by taking into account the radial variation of the monomer concentration $phi$ (r). for an isolated star when increasing r (at the center of the star r $equals$ 0), the variation of $phi$ (r) is first given by a constant value (r $less than$ f**1**/**2 l) then has a (r/1)** $minus$ **1 variation (for f**1**/**2 l $less than$ r $less than$ f**1**/**2 $upsilon$ ** $minus$ **1 l) and finally a(r/l)** $minus$ **4**/**3 variation (for r $greater than$ f**1**/**2 $upsilon$ ** $minus$ **1 l); where f is the number of branches, n the number of monomers in a branch and $upsilon$ and l are the excluded volume and the length associated to a monomer. for all these cases, it is shown that the size of a branch is always larger than that of a linear polymer made of n monomers. beyond the overlapping concentration the star conformation is obtained from two characteristic lengths essentially: $chi$ (c) a radius inside which the branches of the other stars do not penetrate, this radius defines a domain where the conformation of a star is similar to that of an isolated one. beyond $chi$ (c) the interpenetration of branches is characterized by a screening length $xi$ (c) very similar to that for semi-dilute solutions of linear polymers. for all these regimes the variation of the size of a star is predicted as a function of n, f, $upsilon$ and c. 23 refs